Nonexistence of Solutions of a Semilinear Biharmonic Equation with Singular Potential

Sh. G. Bagyrov<sup>ab

a</sup> Baku State University
^b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku

Abstract: The nonexistence of a global solution of the semilinear elliptic equation $\Delta^{2}u-(C/|x|^{4})u-|x|^{\sigma}|u|^{q}=0$ in the exterior of a ball is studied. A sufficient condition for the nonexistence of a global solution is established. The proof is based on the test function method.

Keywords: semilinear elliptic equation, biharmonic operator, global solution, critical exponent, test function method.

UDC: 517.9

Received: 15.12.2016

DOI: 10.4213/mzm11498

 English version: Mathematical Notes, 2018, 103:1, 24–32

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